Dynamic Asset Allocation - Stanford University

Dynamic Asset Allocation

Using Stochastic Programming and Stochastic Dynamic Programming Techniques

Gerd Infanger

Stanford University

Winter 2011/2012

MS&E348/Infanger

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Outline

? Motivation ? Background and Concepts ? Risk Aversion ? Applying Stochastic Dynamic Programming

? Superiority of Dynamic Strategies

? Applying Multi-Stage Stochastic Programming ? Summary

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Asset Allocation

? Allocation between asset classes accounts for the major part of return and risk of a portfolio

? Equity investments ? Interest-bearing investments

? Selection of individual instruments is a lower-level decision with much smaller influence on portfolio performance

? Asset Allocation should consider all financial aspects

? Current and future wealth, income, and financial needs ? Financial goals ? Liquidity (plan for the unexpected)

? Financial industry suggests that investors need customized investment strategies

Winter 2011/2012

MS&E348/Infanger

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Typical Financial Advice

? Questionnaires to assess the risk aversion of an investor

? (E*Trade, Charles Schwab, Fidelity, Financial Engines, ASI, etc...) ? Taking measure, often with great sophistication and much detail ? => risk aversion of the investor (typically assuming constant relative risk

aversion, CRRA)

? Choose from standardized portfolios:

? Conservative, e.g., 20% stocks ? Dynamic, e.g., 40% stocks ? Progressive, e.g., 60% stocks

? Is that a customized portfolio?

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Financial Advice (cont.)

? More recently life-cycle funds have emerged

? E.g., Fidelity Freedom 2020 ? Asset allocation is purely time-dependent

? Often practiced rule of thumb: % stocks = 100 ? age ? But these strategies do not depend on wealth, expected performance,

cash flow, etc.

Winter 2011/2012

MS&E348/Infanger

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Multi-Period Investment

Asset classes

Returns process

Stocks Bonds

Cash

W0

W1

W2

t=0

t=1

t=2

(Network formulation based on John Mulvey (1989))

Winter 2011/2012

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WT Max u (WT)

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Utility

? A utility function is an integrating measure, assigning a value (utility) to each point (possible outcome) of the distribution of returns or wealth.

? Maximizing expected utility is equivalent to choosing a certain distribution (of return or wealth) from all possible obtainable distributions.

? Risk measures, like mean, standard deviation, Sharpe ratio, downside risk, value at risk, etc., are all quantities describing various aspects of a distribution.

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Dynamic Asset Allocation

? In real life investors change their asset allocation as time goes on and new information becomes available.

? In theory investors value wealth at the end of the planning horizon (and along the way) using a specific utility function and maximize expected utility.

? Fixed-mix strategies are optimal only under certain conditions. ? In general and in most practical cases the optimal investment strategy

is dynamic and reflects real-life behavior.

Winter 2011/2012

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